Explicit finite difference schemes adapted to advection–reaction equations

Abstract

Several numerical methods are presented that have been adapted for a linear, first-order, hyperbolic partial differential equation—the non-homogeneous constant coefficient one-way advection–reaction equation. This equation is solved exactly when the non-homogeneous part is a polynomial in time and/or space. The convergence properties of stability and consistency are analysed when these schemes are applied to this equation. Finally, it is shown that these methods produce very good results when applied to other nonlinear problems.

^†A version of this paper was presented at the Sixth International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2006), Universidad Rey Juan Carlos, Madrid.

Keywords:

• Advection–reaction equations
• Explicit finite difference schemes
• Numerical stability
• Truncation error
• Numerical examples

Acknowledgements

This work was supported by Grant SA024/04 from Junta Castilla y León.

Notes

^†A version of this paper was presented at the Sixth International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2006), Universidad Rey Juan Carlos, Madrid.